What does FOIL stand for in mathematics?

FOIL stands for First, Outer, Inner, Last, and it is a mnemonic used to help remember the steps for multiplying two binomials. When you apply the FOIL method, you take the first terms from each binomial, multiply them together, then take the outer terms, followed by the inner terms, and finally the last terms from each binomial, multiplying each pair and adding the results together.

For example, if you're multiplying (a + b)(c + d), using FOIL involves:

• First: Multiply the first terms (a * c).

• Outer: Multiply the outer terms (a * d).

• Inner: Multiply the inner terms (b * c).

• Last: Multiply the last terms (b * d).

This method provides a structured approach to ensure that all combinations of terms are accounted for, resulting in a correct polynomial expansion. Understanding FOIL is fundamental in algebra, especially when dealing with polynomial expressions, as it lays the groundwork for more complex operations.